※ 引述《tiyico (宏)》之銘言：
: xy(x^2-y^2)
: { ------------- (x,y) =/= (0,0)
: 01. f(x,y) ={ x^2+y^2
: {
: 0 (x,y) = (0,0)
: then f (0,0) = ? f (0,0) = ?
: xy yx
: x^2 y^2 z^2
: 02. Let R be the region inside the ellipsiod ----- + ----- + ----- = 1
: a^2 b^2 c^2
: (a,b,c >0)
: and above the plane z = b-y, then the volumn of the region R is ??
: x^2˙sin(1/x)
: 03. lim ------------- (我算0但是不確定耶..)
: x->0 tanx
(x^2)(sin(1/x))
lim -----------------
x->0 tanx
x 1
= lim (------)((x)(sin(---))
x->0 tanx x
x 1
= (lim ------)(lim (x)(sin(---)))
x->0 tanx x->0 x
1 1
= (lim ----------)(lim (x)(sin(---)))
x->0 (secx)^2 x->0 x
= 1*0 = 0
P.S. 0 ≦ |sin(1/x)| ≦ 1
0 ≦ |(x)(sin(1/x))| ≦ |x|
lim 0 ≦ lim |(x)(sin(1/x))| ≦ lim |x|
x->0 x->0 x->0
因為 lim 0 = 0 = lim |x|
x->0 x->0
所以由夾擠定理得知
lim |(x)(sin(1/x))| = 0 => lim (x)(sin(1/x)) = 0
x->0 x->0
: 1 sin(πx^2) 1
: 04. prove 0 < ∫ ---------- dx < ---ln2
: -1/√2 x 2
: 沒頭緒
: 感激賜教了
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